Rufus Fraanje

Centralized and decentralized control of structural vibration and sound radiation

This paper examines the performance of centralized and decentralized feedback controllers on a plate with multiple colocated velocity sensors and force actuators. The performance is measured by the reduction in either kinetic energy or sound radiation, when the plate is excited with a randomly distributed, white pressure field or colored noise. The trade-off between performance and control effort is examined for each case. The controllers examined are decentralized absolute velocity feedback, centralized absolute velocity feedback control and linear quadratic Gaussian (LQG) control. It is seen that, despite the fact that LQG control is a centralized, dynamic controller, there is little overall performance improvement in comparison to decentralized direct velocity feedback control if both are limited to the same control effort.

Convergence analysis of the filtered-U LMS algorithm for active noise control in case perfect cancellation is not possible

The Filtered-U LMS algorithm, proposed by Eriksson for active noise control applications, adapts the coefficients of an infinite-impulse response controller. Conditions for global convergence of the Filtered-U LMS algorithm were presented by Wang and Ren (Signal Processing, 73 (1999) 3) and Mosquera and Perez-Gonzalez (Signal Processing, 80 (2000) 5) for the case where perfect noise cancellation is achievable, which means only measurement noise remains. This, paper shows that the assumption of perfect cancellation is not necessary. In real situations perfect cancellation is often not achievable due to delays and non-minimum phase zeros. The conclusion is derived by analysis of the structure of the Wiener optimal solution. This also leads to the suggestion of preconditioning filters in the Filtered-U LMS updating. The preconditioning has shown considerable increase of the convergence rate in a realistic simulation study.

Extracting hysteresis from nonlinear measurement of wavefront-sensorless adaptive optics system.

In many scientific and medical applications wavefront-sensorless adaptive optics (AO) systems are used to correct the wavefront aberration by optimizing a certain target parameter, which is nonlinear with respect to the control signal to the deformable mirror (DM). Hysteresis is the most common nonlinearity of DMs, which can be corrected if the information about the hysteresis behavior is present. We report a general approach to extract hysteresis from the nonlinear behavior of the adaptive optical system, with the illustration of a Foucault knife test, where the voltage-intensity relationship consists of both hysteresis and some memoryless nonlinearity. The hysteresis extracted here can be used for modeling and linearization of the AO system.

Extremely fast focal-plane wavefront sensing for extreme adaptive optics

We present a promising approach to the extremely fast sensing and correction of small wavefront errors in adaptive optics systems. As our algorithms computational complexity is roughly proportional to the number of actuators, it is particularly suitable to systems with 10,000 to 100,000 actuators. Our approach is based on sequential phase diversity and simple relations between the point-spread function and the wavefront error in the case of small aberrations. The particular choice of phase diversity, introduced by the deformable mirror itself, minimizes the wavefront error as well as the computational complexity. The method is well suited for high contrast astronomical imaging of point sources such as the direct detection and characterization of exoplanets around stars, and it works even in the presence of a coronagraph that suppresses the diffraction pattern. The accompanying paper in these proceedings by Korkiakoski et al. describes the performance of the algorithm using numerical simulations and laboratory tests.

Semidefinite programming for model-based sensorless adaptive optics

Wavefront sensorless adaptive optics methodologies are widely considered in scanning fluorescence microscopy where direct wavefront sensing is challenging. In these methodologies, aberration correction is performed by sequentially changing the settings of the adaptive element until a predetermined image quality metric is optimized. An efficient aberration correction can be achieved by modeling the image quality metric with a quadratic polynomial. We propose a new method to compute the parameters of the polynomial from experimental data. This method guarantees that the quadratic form in the polynomial is semidefinite, resulting in a more robust computation of the parameters with respect to existing methods. In addition, we propose an algorithm to perform aberration correction requiring a minimum of N+1 measurements, where N is the number of considered aberration modes. This algorithm is based on a closed-form expression for the exact optimization of the quadratic polynomial. Our arguments are corroborated by experimental validation in a laboratory environment.

Brief paper: Linear computational complexity robust ILC for lifted systems

In this paper we propose a new methodology to synthesize and implement robust monotonically convergent ILC for lifted systems, with the computational complexity that is linear in the trial length. Starting from the model uncertainty of the local sample to sample LTI or LTV models, and using the randomized algorithm, we compute the bound on the model uncertainty of the ILC system representation in the trial domain (lifted ILC). Based on this computed uncertainty bound, we design weighting matrices of the Norm Optimal ILC, such that the robust monotonic convergence condition is satisfied. Since we compute the uncertainty bound, rather than assuming its value in the trial domain, we reduce the conservatism of the robust design. The linear computational complexity of the algorithms for computation of the uncertainty bound and implementation of the Norm Optimal ILC law, is achieved through exploiting the sequentially semi-separable structure of the lifted system matrices. Therefore the framework proposed in this paper is especially suitable for the LTI and LTV uncertain systems with a large number of samples in the trial. We have performed numerical experiments to demonstrate the robustness and linear computational complexity of the proposed method.

Model-based aberration correction in a closed-loop wavefront-sensor-less adaptive optics system

In many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront measurement in WFSless AO systems imposes a challenge to achieve efficient aberration correction. This paper presents an aberration correction approach for WFSlss AO systems based on the model of the WFSless AO system and a small number of intensity measurements, where the model is identified from the input-output data of the WFSless AO system by black-box identification. This approach is validated in an experimental setup with 20 static aberrations having Kolmogorov spatial distributions. By correcting N=9 Zernike modes (N is the number of aberration modes), an intensity improvement from 49% of the maximum value to 89% has been achieved in average based on N+5=14 intensity measurements. With the worst initial intensity, an improvement from 17% of the maximum value to 86% has been achieved based on N+4=13 intensity measurements.

A spatial canonical approach to multidimensional state-space identification for distributed parameter systems

State-space model identification methods for 1-dimensional (1D) systems cannot be straightforwardly generalized to the multidimensional case, due to the problem of estimating a spatially structured global state sequence. This paper proposes a particular apriori structured state, such that a series of local 1D models obtained can be identified separately.

Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering

Efficient and optimal prediction of frozen flow turbulence using the complete observation history of the wavefront sensor is an important issue in adaptive optics for large ground-based telescopes. At least for the sake of error budgeting and algorithm performance, the evaluation of an accurate estimate of the optimal performance of a particular adaptive optics configuration is important. However, due to the large number of grid points, high sampling rates, and the non-rationality of the turbulence power spectral density, the computational complexity of the optimal predictor is huge. This paper shows how a structure in the frozen flow propagation can be exploited to obtain a state-space innovation model with a particular sparsity structure. This sparsity structure enables one to efficiently compute a structured Kalman filter. By simulation it is shown that the performance can be improved and the computational complexity can be reduced in comparison with auto-regressive predictors of low order.

Adaptive and real-time optimal control for adaptive optics systems

An optimal control method to reject turbulence-induced wavefront distortions in an Adaptive Optics system is discussed. Details of a data-driven control approach are presented where the emphasis is put on the estimation of the optimal predictor of the wavefront disturbance. Several algorithms capable of finding the predictor parameters from the sensor signals are discussed. These algorithms could also track time-varying disturbance characteristics in an adaptive control setting. In a simulation experiment with turbulence data recursive type and batch-wise estimation algorithms are compared.